The bulletin of mathematical biophysics

, Volume 22, Issue 3, pp 285–307 | Cite as

Molecular set theory: A mathematical representation for chemical reaction mechanisms

  • Anthony F. Bartholomay


The present investigation is part of a program aimed at examining the mathematical basis of reaction rate theory (Bartholomay,Bull. Math. Biophys. 20, 1958) from the point of view of individual molecular events. Certain inconsistencies resulting from the classical procedure of using stoichiometric “chemical equations” to represent the kinds of mechanisms involved are pointed out and remedies are suggested by the introduction of set-theoretic notation within the framework of a so-calledMolecular Set Theory. It is concluded that whereas ordinary algebra is a suitable basis for stoichiometry, in discussing mechanisms of chemical reactions,molecular set theory is more appropriate. This is a theory of material transformations which is patterned afterabstract set theory: the individual molecules of a chemical species and chemical transformations from one species to another correspond to the abstract concepts of elements or points of a set and their mappings into other sets respectively. The new notions ofexact molecular sequences andequivalence classes of molecules arising from this study of chemical reactions may be of purely mathematical interest when referred back to the context of abstract set theory.


Equivalence Class Deterministic Theory Unimolecular Reaction Unimolecular Decomposition Reaction Rate Theory 
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Copyright information

© University of Chicago 1960

Authors and Affiliations

  • Anthony F. Bartholomay
    • 1
    • 2
    • 3
  1. 1.Harvard UniversityBoston
  2. 2.The Biophysics Research Laboratory of the Department of Medicine, Harvard Medical SchoolBostonUSA
  3. 3.Peter Bent Brigham HospitalBostonUSA

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